Multiplying Out Single Brackets.

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# Multiplying Out Single Brackets. - PowerPoint PPT Presentation

Multiplying Out Single Brackets. 5 X ( 2X + &amp; ) = 10 X ………. What Does Multiplying Out A Bracket Mean ?. Consider this rectangle broken into two areas as shown:. 6. A1. A2. We are going to work out the area of this rectangle :. x. 2. Area = length  breadth. 6x. + 12. A1 =. 6.

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Presentation Transcript
Multiplying Out Single Brackets.

5 X ( 2X + & )

= 10 X ………

What Does Multiplying Out A Bracket Mean ?

Consider this rectangle broken into two areas as shown:

6

A1

A2

We are going to work out the area of this rectangle :

x

2

6x

+ 12

A1 =

6

x

= 6x

Total Area =

A2 =

6

2

= 12

Now consider the expression below:

Golden Rule:

Everything inside the bracket

must be multiplied by the

Number or term outside the bracket.

6 ( x + 2 )

=

6x

+

12

The same as the area of the rectangle.

Now multiply out the following brackets:

(1) 4 ( x + 6 )

(2) 7 ( 2 x + 5 )

(3) 5 ( 8x + 9 )

= 4x

+ 24

=

14x

+35

=

40x

+ 45

What Goes In The Box 1?

Multiply out the brackets below :

(1) 6 ( x + 3 )

=

6x

+

18

(2) 3 ( 2x + 5 )

=

6x

+

15

(3) 4 ( 6x + 7 )

=

24x

+

28

(4) 9 ( 3x + 9 )

=

27x

+

81

(5) 2 ( 3x + 4 )

=

6x

+

8

(6) 8 ( 5x + 7 )

=

40x

+

56

Some Algebra Revision.

You should know the answer to the following questions:

Multiply out :

Calculate :

(1) 2y  5 y =

10y 2

(1) 3  - 4 =

-12

(2) 3w  4 w =

12w 2

(2) 6  - 7 =

- 42

(3) 6r  7r =

42r 2

(3) - 3  8 =

- 24

(4) 4f  3f =

12f 2

(4) 7  - 6 =

- 42

(5) 9h  8h =

72h 2

(5) - 8  2 =

- 16

Harder Single Brackets.

Multiply out the brackets below:

(1) 3t ( 2t + 6 ) =

6t 2

+

18t

28w

(2) 4w ( 3w - 7 ) =

12w 2

-

(3) 5a ( 2a + 9 ) =

10a 2

+

45a

(4) 2z ( 5z - 8 ) =

10z 2

-

16z

What Goes In The Box 2 ?

(1) 3x ( 4x – 7 ) =

12x 2

21x

(2) 6w ( 8w + 3 ) =

48w 2

+

18w

(3) 2f ( 3f - 5 ) =

6f 2

10f

(4) 8r ( 6r + 3 ) =

48r 2

+

24r

(5) 3d ( 5d - 9 ) =

15d 2

27d

(6) 8a ( 9a + 3 ) =

172a2

+

24a

More Than One Bracket.

Consider the brackets below:

Multiply out both brackets:

2( 3x + 6 ) + 2 ( 4x + 3 )

Gather like terms together.

= 6x + 12 + 8x + 6

= 6x + 8x + 12 + 6

= 14x + 18

You have now multiplied out the brackets and simplified the expression.

Multiply out the brackets below and simplify :

4 ( 3x – 5 ) + 2 ( 3x – 7 )

Solution.

4 ( 3x – 5 ) + 2 ( 3x – 7 )

= 12x – 20 + 6x – 14

= 12x + 6x – 20 – 14

= 18x – 34

Remember that a negative times a negative makes a positive.

Multiply out the brackets below and simplify :

4 ( 2 b + 5 ) – 6 ( 3b – 4 )

Solution

4 ( 2 b + 5 ) – 6 ( 3b – 4 )

= 8b + 20 – 18b + 24

= 8b – 18 b + 20 + 24

= – 10 b + 44

What Goes In The Box 3 ?

Multiply out and simplify the brackets below:

(1) 2 ( x + 4 ) + 3 ( x + 5)

(5) 2 ( 3g – 4 ) + 2 ( 4g – 6 )

= 5x +23

= 14g -20

(2) 3 ( 2a + 5 ) + 4 ( 3a + 3 )

(6) 5 ( 3f – 6 ) – 4( 2 f – 6 )

= 7f – 6

= 18a + 27

(7) 3 ( 4t – 6 ) – 7 ( 6t – 8)

( 3) 4 ( 5b + 2 ) + 3 ( 2b + 7)

= 26b + 29

= - 30t + 38